Mathematics is a notation for the study of number, quantity, shape and space - which for me is why it is an art - it is completely created by people, unlike concrete which is a mix of water, aggregate and cement (sorry for being facetious).

If I write 3 + 4 = 12 and you say no it isn't, I am empirically wrong. That's math.

That might be wrong in base 10 but actually it's correct in base 5 (luckily you chose a sum that is correct in base 5 :~D) - who is wrong? We have failed to communicate our notation - hopefully without the catastrophic consequences of the Mars Climate Orbiter.

I agree that mathematics should not be subjective, and that 1 + 1 = 2 - but that proof took three volumes by Bertrand Russell and Alfred Whitehead?